Ind. Eng. Chem. Res. 2004, 43, 1523-1529
1523
GENERAL RESEARCH Experimental and Predicted Solubilities of HFC134a (1,1,1,2-Tetrafluoroethane) in Polyethers Enriqueta R. Lo´ pez,† Ana M. Mainar,‡ Josefa Garcı´a,†,§ Jose´ S. Urieta,‡ and Josefa Ferna´ ndez*,† Group of Applied Thermodynamics and Surfaces (GATHERS), Aragon Institute for Engineering Research (I3A), Facultad de Ciencias, Universidad de Zaragoza, 50009 Zaragoza, Spain, Laboratorio de Propiedades Termofı´sicas, Departamento de Fı´sica Aplicada, Facultad de Fı´sica, Universidad de Santiago, 15782 Santiago de Compostela, Spain, and Departamento de Fı´sica Aplicada, Facultad de Ciencias, Universidad de Vigo, 36200 Vigo, Spain
Experimental solubilities were determined for 1,1,1,2-tetrafluoroethane (HFC134a) in triethylene glycol dimethyl ether and in tetraethylene glycol dimethyl ether at 101.33 kPa refrigerant partial pressure in the low-temperature range (258.15-298.15 K). The experimental device was adapted from an apparatus commonly used to measure slightly soluble gases. Because HFC134a was highly soluble in the two polyglycols, the mole fraction of the refrigerant was calculated by the φ-γ method and the symmetrical criteria for the components. The solubilities of the refrigerant in the two solvents were very similar. The thermodynamic quantities related to the solution process were also obtained from the solubility data. The isobaric solubilities predicted by the original and Dortmund UNIFAC versions were compared with the experimental values to test the interaction parameters of Kleiber (Fluid Phase Equilib. 1995, 107, 161) and Kleiber and Axmann (Comput. Chem. Eng. 1998, 23, 63). Introduction The restrictions imposed on the use of chlorofluorocarbons as working fluids in heat pumps and refrigeration systems have stimulated the search for alternative refrigerants, such as 1,1,1,2-tetrafluoroethane (HFC134a) and other hydrofluorocarbons (HFCs), methanol, and 2,2,2-trifluoroethanol.1-3 In this context, one of the most important tasks is to find compressor lubricants compatible with the alternative refrigerants.4,5 This requires information about thermophysical properties of the refrigerant, lubricant and mixtures such as density, viscosity, vapor pressure, miscibility, heat of mixing, heat capacity or thermal conductivity; and solubility of the refrigerant in the lubricant. However, it has been found that the mutual miscibilities of conventional lubricating oils [i.e., mineral oil, poly(R-olefin), alkylbenzene, etc.] and HFC refrigerants are quite poor, thus leading to poor performances of the refrigerating devices. To avoid this, poly(alkylene glycol) (PAG), polyol ester (POE), and other new lubricants have been developed for commercial applications with HFCs and blends of HFCs with other refrigerants.4 In recent years, experiments have been carried out using PAG-type compounds as compressor lubricants with HFC134a.6 Some useful PAGs are poly(ethylene * To whom correspondence should be addressed. tel.: +34 981 563 100 (ext. 14046). Fax: +34 981 520 676. E-mail:
[email protected]. † Universidad de Santiago de Compostela. ‡ Universidad de Zaragoza. § Universidad de Vigo.
glycol) dimethyl ethers, CH3O-[(CH2)2O]n-CH3, because they are thermally and chemically stable, with much higher boiling points than alternative refrigerants proposed for absorption cycles. Moreover, dimethyl ether functional groups have an advantageous strong affinity for the small polar molecules of refrigerants. Tseregounis and Riley6 have measured the solubility of HFC134a in several glycol-type compounds (glycols and glycol derivatives), concluding that the PAG tetraethylene glycol dimethyl ether (TEGDME, n ) 4) shows a higher ability to dissolve HFC134a. According to these authors, this fact is the result of eliminating the free OH group from glycol compounds. Moreover, water is less soluble in the ether than in the original glycol. Recently, Coronas et al.7 measured the vapor-liquid equilibrium (VLE) of HFC134a + triethylene glycol dimethyl ether (TrEGDME, n ) 3) in a temperature range of 283.15-353.15 K using a static method. No data have been published for HFC134a + TrEGDME or TEGDME at temperatures below 283.15 K, even though these working conditions are remarkably important in many applications, such as absorption systems.8 In this paper, we report the solubilities of the refrigerant 1,1,1,2-tetrafluoroethane (HFC134a) in triethylene glycol dimethyl ether and tetraethylene glycol dimethyl ether at 101.33 kPa partial pressure of gas and a range of temperatures (258.15-298.15 K). Because these solubilities are rather large, we modified and tested an existing Ben-Naim-type apparatus,9 previously used to measure slightly soluble gases in pure and mixed organic solvents. We also calculated several
10.1021/ie030623w CCC: $27.50 © 2004 American Chemical Society Published on Web 02/14/2004
1524 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004
Figure 1. Sketch of the solubility apparatus: VP, vacuum pump; LNT, liquid nitrogen trap; TB, thermostated bath; SV, solution vessel; M, manometer; MS, magnetic stirrer; BS, buret system; SM, mercury storage; TAB, thermostated air bath.
thermodynamic quantities related to the solution process from the experimental solubility data, namely, the Gibbs energy, enthalpy, and entropy of solution. These measurements are also valuable in evaluating and developing a predictive model because few authors have measured the solubilities of HFCs in compressor oils consisting of only one substance with a known structure.10,11 We chose the UNIFAC model (original and Dortmund versions), because it is currently the best-known group contribution model and the most frequently used to predict phase equilibrium. We tested the UNIFAC parameters calculated by Kleiber12 and Kleiber and Axmann13 for the original and Dortmund versions, respectively, by comparing the experimental data reported in this work with the values calculated using these parameters. Experimental Section Materials. HFC134a (Forane 134a, mole fraction > 0.997) was supplied by Air Liquide. TrEGDME and TEGDME (Aldrich, mole fraction > 0.99) were not purified further, other than being dried with Union Carbide 0.4-nm molecular sieves (Fluka) and degassed under vacuum before use. Procedure. Measurements were made using a volumetric method with an apparatus9 based on that of BenNaim and Baer14 made of glass with Teflon valves. We have used this apparatus widely to measure solubilities of slightly soluble gases (He, Ne, Ar, Kr, Xe, N2, H2, D2, O2, CH4, C2H6, C2H4, CF4, SF6, and CO2) in an extensive series of single organic compounds15-18 and liquid mixtures.19 As shown in Figure 1, the experimental equipment consists of a solution vessel, a buret system, and a mercury manometer to measure and control the pressure with a cathetometer, WILD KM 338 ((2.7 × 10-3 kPa). The amount of solvent used is weighed after degassing ((1 × 10-4 g). The solution vessel is immersed in a thermostatic liquid bath ((0.05 K), and the whole apparatus is placed in a thermostated air bath ((0.2 K) at a temperature higher than that of the liquid to prevent condensation of the vapor solvent outside the solution vessel. The total volume of the gas line is 253 cm3. The experimental technique is based on determining the volume ((0.2 cm3) of the gas phase that dissolves
in a known mass of solvent at constant temperature and pressure. The amount of gas saturated with vapor transferred to the solvent is measured through the volume of mercury introduced into the buret system to keep the pressure balanced. The relative expanded uncertainty in the solubility measurements, expressed as mole fractions and Ostwald coefficients, was estimated from the precision in the measurements of the volume, pressure, and temperature in the gas phase and the mass and density ((10-5 g cm-3) of the solvent. The uncertainty calculations were simplified by considering ideal behavior of the gas phase, and a coverage factor of 2 was applied. The mean values for the relative uncertainties were above 1% for the mole fraction and the Ostwald coefficient. Because of the specific features of the HFC134a + PAG mixtures, two main problems had to be overcome. The first was related to the high solubility of the refrigerant in the glycols and the second to the wide gradient of temperatures between the liquid bath and the air bath when measurements were carried out below 268.15 K. With respect to temperature stabilization, a thermal insulator was used to keep heat out of the refrigerant glass bath. A small window was cut in the thermal insulator for control of the experiment. Despite the temperature gradient, the insulation cover kept the temperature of the liquid bath constant within (0.05 K. On the other hand, the vessel had to be redesigned to handle the high solubilities of the refrigerant in the lubricants. A smaller vessel (15 cm3 capacity) with a Teflon stopcock was made by the Glass Blowing Service at the University of Zaragoza, Spain. Using this design, we could work within the device range for dissolved gas volumes and prevent diffusion phenomena before saturation. Because the vessel was so small, it was made without the usual lateral branch,14 and therefore, the time to saturation was quite long (20-30 h per point). The solubility of the refrigerant is expressed in terms of the Ostwald coefficient and also as a mole fraction. The Ostwald coefficients, defined by the following equation
L ) (Vg/Vs)T
(1)
were determined from the volume of gas dissolved, Vg, and the volume of the pure solvent used, Vs, at the temperature of the vessel, T, and 101.33 kPa. Volumes from 45 to 185 cm3 of refrigerant were dissolved in the polyethers depending on the temperatures. To express the solubilities as mole fractions, we considered the nonideal behavior of the gas phase and calculated the gas solubilities from the experimental data by applying a reduction method obtained from Wilhelm20 and Tseregounis and Riley.6 Briefly, the data reduction procedure involved several iterations to determine the number of moles of gas transferred from the burets to the solution vessel using the φ-γ method and the symmetrical criteria for the standard states of both the solute and the solvent. The mole fraction of gas at total pressure P (close to 101.33 kPa) and working temperature T was calculated using the second virial coefficients for the gas phase and considering ideal gas behavior in the zeroth-order iteration.21 Then, the activities of the components in the
Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1525 Table 1. Experimental Densities of TrEGDME and TEGDME at 268.15 and 273.15 K and Parameters of the Equationa Correlated On the Basis of Experimental Data and Values from the Literature24,25 F (kg m-3) solvent
268.15 K
273.15 K
TrEGDME TEGDME
1011.7 1035.0
1006.2 1030.3
solvent TrEGDME TEGDME a
A0 1344.5 1315.3
A1 1.450 1.132
TrEGDME
r2
A2 10-4
7.71 × 3.24 × 10-4
Table 2. Activity Coefficients of the Refrigerant, γr, and Solubilities of HFC134a in TrEGDME and TEGDME Expressed in Terms of the Mole Fraction, xr, of HFC134a in the Solution and as the Ostwald Coefficient, L ) (Vg/Vs)T
0.9997 0.9999
F (kg m-3) ) A0 + A1T + A2T 2.
TEGDME
T (K)
xr
γr
L
xr
γr
L
258.15 263.15 268.15 273.15 278.15 288.15 298.15
0.6831 0.6298 0.5455 0.4656 0.3976 0.2911 0.2168
0.9291 0.8341 0.8037 0.7925 0.7876 0.7934 0.8088
264.3 203.4 144.0 106.0 81.5 51.7 36.0
0.7054
0.8998
226.1
0.5510 0.4770 0.4080 0.3015 0.2295
0.7957 0.7736 0.7674 0.7661 0.7641
124.0 92.2 70.1 45.8 32.2
liquid phase were estimated through the isofugacity condition for both components /V PyiφVi (T,P,yi) ) xiγi(T,P,xi) Ps,i(T) φs,i (T,Ps,i) P(P,T) (2)
where xi and yi are the mole fractions of the liquid and gas phases, respectively; φVi is the fugacity coefficient /V is the fugacity coefficient of satuof component i; φs,i rated pure component i; Ps,i is the vapor pressure of component i; P is the Poynting correction; and γi is the activity coefficient of liquid component i according to the Lewis-Randall rule. Finally, from the mole fraction of gas at the given total pressure, the solubility values at 101.33 kPa partial pressure of gas were inferred, again using the eq 2 for both components. Several simplifications were made during the trialand-error procedure: (i) A one-parameter Margules equation was used for the small changes in activity coefficients between the working vapor pressure of the refrigerant and the reference pressure of 1 atm. (ii) The fugacity coefficients were estimated from a virial equation truncated after the second term, except for the fugacity coefficient of the saturated vapor of the refrigerant, which was calculated using the REFPROP software package.22 (iii) The Poynting corrections were obtained using the molar volumes of the pure components and Zellner’s method for HFC134a.23 To apply the described method, new values of density for TrEGDME and TEGDME at 268.15 and 273.15 K were measured and correlated with data available in the literature.24,25 The corresponding values were fitted to a second-order polynomial function. The experimental data and adjusted parameters are listed in Table 1. Vapor pressures for all compounds were also taken from the literature.7,26-28 For polyethers, the second virial coefficients were obtained with the Tsonopoulos method,29 whereas for HFC134a, these coefficients were taken from Beckermann and Kholer.30 Results and Discussion Experimental solubilities are reported in Table 2 as mole fractions of gas in the liquid phase and also as Ostwald coefficients at several temperatures and 101.33 kPa partial pressure of the gas. Refrigerant activity coefficients, γr, determined from experimental solubilities are also included in Table 2. The refrigerant is highly and similarly soluble in both polyethers, although it is slightly more soluble in TEGDME. The high solubilities might be caused by specific interactions (probably hydrogen bonding), although
Figure 2. Experimental solubilities of HFC134a in TrEGDME (- -O- -) and in TEGDME (s9s). UNIFAC predictions: original (1) and Dortmund (2).
there could be other effects, such as steric factors or interactions among polar groups. Recently, Bobbo et al.31,32 measured isothermal vapor-liquid equilibria for binary systems involving HFCs and dimethyl ether. They found that HFCs are active proton donors that can form strong H-bonds with proton acceptors. Comun˜as et al.33,34 found similar results regarding the experimental excess volumes of the binary mixtures HFC134a + TrEGDME or TEGDME. The excess volumes had strong negative values, in agreement with the degrees of interaction between unlike molecules of these mixtures, that is, the high affinities of polyethers for HFC134a. We correlated the experimental solubility data using a polynomial in T
ln xr ) A +
B + C ln T T
(3)
where xr is the mole fraction of refrigerant. Figure 2 shows the temperature dependence of the solubilities expressed in terms of the refrigerant mole fraction. A similar equation can be used to fit the refrigerant activity
ln ar ) ln(xrγr) ) A′ +
B′ + C′ ln T T
(4)
The parameters in eqs 3 and 4 calculated from the experimental measurements are reported in Table 3, together with the associated standard deviations, σ.
1526 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 Table 3. Correlations of the Solubility and Activity Data of HFC134a in TrEGDME and TEGDME by Means of Eqs 3 and 4, respectively solvent
A
B
C
σln xa
TrEGDME TEGDME
199.07 149.78
-6434.4 -4440.3
-31.422 -23.935
0.0223 0.0163
solvent
A′
B′
C′
σln aa
TrEGDME TEGDME
-52.962 -53.096
4271.8 4276.9
6.4751 6.4957
0.0008 0.0006
a
σln(x,a) ) [{Σ[ln(xr,ar)exp - ln(xr,ar)cal]2}/(N - NP)]1/2
Figure 4. Solubilities of HFC134a in TrEGDME: comparison between our experimental data (O) and results from a pressure interpolation of the Coronas et al.7 data (×).
Figure 3. Activity coefficients of HFC134a in TrEGDME (O, experimental; - - -, predicted) and in TEGDME (9, experimental; s, predicted) for the equilibrium concentration at several temperatures. UNIFAC predictions: original (1) and Dortmund (2).
The activity coefficients of the refrigerant in the refrigerant/polyether solutions are plotted in Figure 3. These coefficients are clearly temperature-dependent, decreasing monotonically as the temperature is increased for TEGDME but exhibiting a minimum at 273.15 K for TrEGDME. The activity coefficients were less than 1, so all of the mixtures present negative deviations from ideality, which is in agreement with the formation of hydrogen bonds proposed above. To test the validity of the experimental procedure, we compared our solubility data with other values in the literature,6,7,28 although most reported values were measured at different temperatures and pressures. As seen in Figures 3 and 4, our experimental data clearly follow the temperature trend of the previous data series. Our experimental solubility values for HFC134a + TrEGDME (Figure 4) are similar to those of Coronas et al.7 (the deviations being 1.6%), but for HFC134a + TEGDME, the deviations are slightly larger (Figure 5), namely, 11.2 and 6.4% with respect to the results of Tseregounis and Riley6 and to Borde et al.,28 respectively. However, it should be noted that the bibliographic values included in Figure 5 were obtained by extrapolating the original data series to atmospheric pressure. Standard Changes in Thermodynamic Functions of Solution. The solubility of a gas in a liquid is directly related to the difference between the standard chemical potential of the solute in the liquid phase,
Figure 5. Solubilities of HFC134a in TEGDME: comparison between our experimental data (9) and results from pressure extrapolations of the Tseregounis and Riley6 (×) and Borde et al.28 (*) data.
µo,L r , and the standard chemical potential of the solute in the gas phase, µo,G r . Indeed, the equality of chemical potentials for each component in the coexisting phases in equilibrium is expressed by the equation
µLi ) µG i
(5)
Using this equation for the solute (refrigerant, i ) r) and expressing the chemical potential as a function of the activity and the fugacity, we obtain o,G µo,L ) -RT ln r - µr
(xrγr) φrPr
(6)
The left side of eq 6 represents the change in the Gibbs energy, ∆G h or,sol, associated with the ideal solution process for 1 mol of solute35,36
A(hypothetical gas,101.33 kPa,T) f A(P,T,hypothetical solution,xr ) 1)
Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1527 Table 4. Thermodynamic Functions of Solution of the Refrigerant HFC134a in Both Polyethers TrEGDME
TEGDME
T (K)
o ∆G h r,sol (kJ mol-1)
o ∆H h r,sol (kJ mol-1)
258.15 263.15 268.15 273.15 278.15 288.15 298.15
0.97 1.41 1.84 2.26 2.68 3.51 4.32
-21.61 -21.35 -21.08 -20.81 -20.54 -20.00 -19.47
(J
o ∆S h r,sol mol-1 K-1)
-87.50 -86.47 -85.46 -84.47 -83.50 -81.60 -79.78
assuming ideal behavior for both phases. In our case, the fugacity of the gas is close to 101.33 kPa, so the solution Gibbs energy of the solute can be calculated as
T (K)
o ∆G h r,sol (kJ mol-1)
o ∆H h r,sol (kJ mol-1)
o ∆S h r,sol (J mol-1 K-1)
258.15
0.98
-21.61
-87.50
268.15 273.15 278.15 288.15 298.15
1.84 2.26 2.68 3.51 4.32
-21.07 -20.81 -20.54 -20.00 -19.46
-85.45 -84.46 -83.48 -81.58 -79.75
Table 5. Solubilities of HFC134a in TrEGDME and TEGDME Predicted by the UNIFAC Model, Expressed in Terms of the Mole Fraction xr TrEGDME
TEGDME
UNIFAC
∆G h or,sol ) -RT ln(xrγr)
(7)
According to eq 4, we obtain
∆G h or,sol
B′ + C′ ln T ) -RT A′ + T
(
)
(8)
The so-called enthalpy and entropy of solution are obtained from the Gibbs energy using the well-known relationships from classical thermodynamics
∆H h or,sol
) -T
∆S h or,sol )
[
2
]
∂(∆G h or,sol/T) ∂T
p
[
) RT
]
∂ ln (xrγr) ) ∂ ln T p - RB′ + RTC′ (9)
∆H h or,sol - ∆G h or,sol ) RA′ + RC′(1 + ln T) (10) T
We calculated the three thermodynamic quantities related to the solution process (Table 4). Few differences were found between the two systems as the solubilities are similar. When compared with the most common results (corresponding to slightly soluble gases in organic solvents) of these quantities, the values obtained in the present work for ∆G h or,sol are smaller (∼5 times), and those for o ∆H h r,sol are much higher (∼10 times) and negative.15,37 This is a consequence of the high solubilities of the refrigerant in the polyethers. Application of the UNIFAC Model. The interaction coefficients of several group contribution models need to be determined to predict the properties of the mixtures and obtain the phase diagrams when no reliable experimental data are available. Once determined, the performances of these models must be verified by comparing the model results with new experimental data. We make such a verification of parameters for several fluorinated groups. Currently, the only group contribution models for which interaction parameters12,13 applicable to HFCs are available are two versions of the UNIFAC model, the original38 and Dortmund39 versions. Kleiber12 extended the original version of UNIFAC to common refrigerants by taking into account all previously published vapor-liquid equilibria data points for binary mixtures containing fluorinated hydrocarbons. Thus, the interaction parameters were determined for 10 new groups that describe the forms of several halogenated refrigerants.
UNIFAC
T (K)
original
Dortmund
T (K)
original
Dortmund
258.15 263.15 268.15 273.15 278.15 288.15 298.15
0.7615 0.6770 0.5987 0.5270 0.4625 0.3551 0.2735
0.8281 0.7467 0.6638 0.5848 0.5131 0.3959 0.3099
258.15
0.7842
0.8467
268.15 273.15 278.15 288.15 298.15
0.6298 0.5596 0.4952 0.3858 0.3004
0.6901 0.6127 0.5416 0.4232 0.3345
Kleiber and Axmann13 used the Dortmund version of UNIFAC for refrigerants, fitting 386 adjustable parameters simultaneously. A conventional gradient method and an evolutionary algorithm were used to determine the parameters. In this paper, we present the solubilities of HFC134a in TrEGDME and TEGDME predicted by the UNIFAC model using the parameters of Kleiber12 for the original version and those of Kleiber and Axmann13 for the Dortmund version. HFC134a (CF3CH2F) was considered to consist of two subgroups: number 155, named (CF3-)CH2F, of the main group 72 (CHF2) and number 157, named (CH2)CF3, of the main group 73 (CHF3). Thus, the (CF3-)CH2F subgroup of HFC134a is different from the CH2F groups of other molecules, and its (CH2-)CF3 subgroup is different from the CF3 groups of perfluoroalkanes, as explained by Kleiber12 in terms of the electronic charges of the subgroups. The TrEGDME (n ) 3) and TEGDME (n ) 4) molecules were considered as in the original UNIFAC model, so a polyether glyme such as CH3O(CH2-CH2O)n-CH3 would have the following subgroups: one CH3, n CH2, n CH2O, and one CH3O. In Figure 3, we plot the predicted results obtained using both UNIFAC versions, together with the experimental results for the activity coefficients, γr, corresponding to the equilibrium concentrations at several temperatures. The sign of the deviations from ideality was predicted correctly by both versions. The differences between the experimental and predicted γr values increased with increasing temperature. The percentage means for the differences were 13% for TrEGDME and 17% for TEGDME with the original version and 22 and 24%, respectively, with the Dortmund version. The solubilities predicted using both UNIFAC versions are included in Table 5 and Figure 2. Obviously, the relative differences between the experimental and theoretical solubilities are the same as for the activity coefficients. Conclusion An experimental device that has been widely used for slightly soluble gases was successfully adapted to
1528 Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004
measure highly soluble compounds such as HFCs in polyglycolethers at low temperatures and atmospheric pressure. According to the data for HFC134a in two polyethers (TrEGDME and TEGDME) at six temperatures and 101.33 kPa partial pressure of gas, solubility increases slightly with the number of ether groups in the polyether molecules. The activity coefficients of HFC134a indicated negative deviations from ideality in the systems investigated because of the high affinities between the solute and solvent molecules. The small changes in the Gibbs energy associated with the solution process in the two systems indicated that the solvation process is thermodynamically favored. The Kleiber parameters of the original UNIFAC model predicted the experimental solubilities better than the Kleiber and Axmann parameters of the Dortmund version of the UNIFAC model. Unfortunately, the predictions obtained using these sets of parameters with both versions of UNIFAC showed significant deviations from the experimental data. This finding has already been verified by several authors19,40 in cases where the parameters are too general for the required application. In the near future, experimental solubilities will be able to be used as a reference to improve old models or test new ones such as cubic EOS + UNIFAC applied to refrigerant-lubricant systems. Acknowledgment This work was partly funded by the Research Projects QUI98-1071-C02-01 CICYT, Spain, and PPQ2001-3022 and PB98-1624 Programa Sectorial, MEC, Spain. A.M.M. thanks SXID (Xunta de Galicia) and the University of Santiago for financial support for two research stays at the University of Santiago. Nomenclature A, B, C, A′, B′, C′ ) adjustable coefficients in eqs 3, 4, and 8-10 A0, A1, A2 ) adjustable density coefficients in Table 1 ∆G h or,sol ) standard partial molar Gibbs energy for the solution process, kJ mol-1 ∆H h or,sol ) standard molar enthalpy for the solution process, kJ mol-1 ∆S h or,sol ) standard molar entropy for the solution process, J mol-1 K-1 L ) Ostwald coefficient N ) total number of points correlated in eqs 2 and 3 NP ) number of adjustable parameters in eqs 2 and 3 P ) total pressure, kPa Ps,i ) vapor pressure of component i, kPa P ) Poynting correction R ) gas constant T ) absolute temperature, K Vg ) volume of dissolved gas, cm3 Vs ) volume of solvent, cm3 ar ) activity of the refrigerant xi ) mole fraction of component i in the liquid phase yi ) mole fraction of component i in the gas phase Greek letters µi ) chemical potential of component i µoi ) standard chemical potential of component i γi ) activity coefficient of component i φi ) fugacity coefficient of component i / ) fugacity coefficient of saturated vapor of pure φs,i component i σ ) standard deviation
Subscripts 1 ) solvent component/glycol r ) solute component/refrigerant cal ) calculated value exp ) experimental value Superscripts o ) standard quantity L ) liquid state V ) vapor state * ) pure compound
Literature Cited (1) Medrano, M.; Bourouis, M.; Coronas, A. Double-Lift Absorption Refrigeration Cycles Driven by Low-Temperature Heat Sources Using Organic Fluid Mixtures as Working Pairs. Appl. Energy 2001, 68, 173. (2) Boer, D.; Valles, M.; Coronas, A. Performance of Double Effect Absorption-Compression Cycles for Air Conditioning Using Methanol-TEGDME and TFE-TEGDME Systems as Working Pairs. Int. J. Refrig. 1998, 21, 542. (3) Levy, A.; Jelinek, M.; Borde, I. Single Stage Absorption System Based on Refrigerants R125 and R134A with DMETEG. Therm. Sci. 2000, 1, 511. (4) Marsh, K. N.; Kandil, M. E. Review of Thermodynamic Properties of Refrigerants + Lubricant Oils. Fluid Phase Equilib. 2002, 199, 319. (5) Spauschus, H. O. Lubricants for Refrigeration Compressors: A 1996 Status Report. Bull. Int. Inst. Refrig. 1997, 97, 3. (6) Tseregounis, S. I.; Riley, M. J. Solubility of HFC-134a Refrigerant in Glycol-type Compounds: Effects of Glycol Structure. AIChE J. 1994, 40, 726. (7) Coronas, A.; Mainar, A. M.; Patil, K. R.; Conesa, A.; Shen, S.; Zhu, S. Solubility of 1,1,1,2-Tetrafluoroethane in Triethylene Glycol Dimethyl Ether. J. Chem. Eng. Data 2002, 47, 56. (8) Jelinek, M.; Borde, I. Single and Double-Stage Absorption Cycled Based on Fluorocarbon Refrigerants and Organic Absorbents. Appl. Therm Eng. 1998, 18, 765. (9) Carnicer, J.; Gibanel, F.; Urieta, J. S.; Gutie´rrez Losa, C. Apparatus for Measurement of Gas Solubility in Liquids. Solubilities of Helium, Deuterium, Nitrogen, and Sulfur Hexafluoride in p-Xylene. Rev. Acad. Cienc. Zaragoza 1979, 34, 115. (10) Wahlstro¨m, A.; Vamling, L. Solubility of HFC32, HFC125, HFC143a, HFC143a and HFC152a in a Pentaerythritol Tetrapentanoate Ester. J. Chem. Eng. Data 1999, 44, 823. (11) Wahlstro¨m, A.; Vamling, L. Solubility of HFCs in Pentaerythritol Tetraalkyl Esters. J. Chem. Eng. Data 2000, 45, 97. (12) Kleiber, M. An Extension to the UNIFAC Group Assignment for Prediction of Vapor-Liquid Equilibria of Mixtures Containing Refrigerants. Fluid Phase Equilib. 1995, 107, 161. (13) Kleiber, M.; Axmann, J. K. Evolutionary Algorithms for the Optimization of Modified UNIFAC Parameters. Comput. Chem. Eng. 1998, 23, 63. (14) Ben-Naim, A.; Baer, S. Method for Measuring Solubilities of Slightly Soluble Gases in Liquids. Trans. Faraday Soc. 1963, 59, 2735. (15) Pardo, J.; Mainar, A. M.; Lopez, M. C.; Royo, F.; Urieta, J. S. Solubility of Gases in Butanols IV. Solubilities of Nonpolar Gases in 2-Methyl-2-propanol at 303.15 K and 101.33 kPa Partial Pressure of Gas. Fluid Phase Equilib. 1999, 155, 127. (16) Gibanel, F.; Lo´pez, M. C.; Royo, F. M.; Pardo; J.; Urieta, J. S. Solubility of 13 Non-Polar Gases (Helium, Neon, Argon, Krypton, Xenon, Hydrogen, Deuterium, Nitrogen, Methane, Ethane, Carbon Tetrafluoride and Sulfur Hexafluoride) in 2-Methyltetrahydrofuran at 273.15 to 303.15 K and 101.33 kPa Partial Pressure of Gas. Fluid Phase Equilib. 1993, 87, 285. (17) Lizano, L. P.; Lo´pez, M. C.; Royo, F. M.; Urieta, J. S. Solubility of Nonpolar Gases in Formaldehyde Diethyl Acetal Between -10 and 30 °C, and 1 atm Partial Pressure of Gas. J. Solution Chem. 1990, 19, 721. (18) Mainar, A. M.; Pardo, J. I.; Garcı´a, J. I.; Royo, F. M.; Urieta, J. S. Solubility of Gases in Fluoroorganic Alcohols Part I. Solubilities of Several Non-Polar Gases in 1,1,1,3,3,3-Hexafluoropropan-2-ol at 298.15 K and 101.33 kPa. J. Chem. Soc., Faraday Trans. 1998, 94, 3595. (19) Mainar, A. M. Estudio Termodina´mico de las Solubilidades de Gases no Polares en Mezclas H2O + 2,2,2-Trifluoroetanol y H2O
Ind. Eng. Chem. Res., Vol. 43, No. 6, 2004 1529 + 1,1,1,3,3,3-Hexafluoropropan-2-ol. Doctoral Thesis, Faculty of Sciences, University of Zaragoza, Zaragoza, Spain, 2000. (20) Wilhelm, E. Precision Methods for the Determination of the Solubility of Gases in Liquids. CRC Crit. Rev. Anal. Chem. 1985, 16, 129. (21) De la Iglesia, O.; Mainar, A. M.; Pardo, J. I.; Urieta J. S. Solubilities of Nonpolar Gases in Triethylene Glycol Dimethyl Ether, Tetraethylene Glycol Dimethyl Ether, Dimethyl Carbonate, and Diethyl Carbonate at 298.15 K and 101.33 kPa Partial Pressure of Gas. J. Chem. Eng. Data 2003, 48, 657. (22) McLinden, M. O.; Klein, S. A.; Lemmon, E. W.; Peskin, A. P. NIST Thermodynamic and Transport Properties of Refrigerants and Refrigerant Mixtures (REFPROP); NIST Standard Database 23, version 6.01; National Institute of Standards and Technology (NIST): Gaithersburg, MD, 1998. (23) Zellner, M. G.; Claitor, L. C.; Prausnitz, J. M. Prediction of vapor-liquid equilibriums and enthalpies of mixtures at low temperatures. Ind. Eng. Chem. Fundam. 1970, 9, 549. (24) Comun˜as, M. J. P.; Baylaucq, A.; Boned, C.; Ferna´ndez, J. High-Pressure Measurements of the Viscosity and Density of Two Polyethers and Two Dialkyl Carbonates. Int. J. Thermophys. 2001, 22, 749. (25) Comun˜as, M. J. P.; Lo´pez, E. R.; Pires, P.; Garcı´a, J.; Ferna´ndez, J. pFT Measurements of Polyethylene Glycol Dimethylethers Between 278.15 and 328.15 K at Pressures to 12 MPa. Int. J. Thermophys. 2000, 21, 831. (26) Chaudhari, S. K.; Patil, K. R.; Allepu´s, J.; Coronas, A. Measurement of the vapor pressure of 2,2,2-trifluoroethanol and tetraethylene glycol dimethyl ether by static method. Fluid Phase Equilib. 1995, 105, 159. (27) CRC Handbook of Chemistry and Physics, 79th ed.; CRC: Boca Raton, FL, 1999. (28) Borde, I.; Jelinek, M.; Daltrophe, N. C. Absorption System Based on the Refrigerant R134a. Int. J. Refrig. 1995, 18, 387. (29) Tsonopoulos, C. Second Virial Coefficients of Water Pollutants. AIChE J. 1978, 24, 1112. (30) Beckermann, W.; Kohler, F. Acoustic determination of ideal-gas heat capacity and second virial coefficients of some refrigerants between 250 and 420 K. Int. J. of Thermophys. 1995, 16, 455.
(31) Bobbo, S.; Fedele, L.; Camporese, R.; Stryjek, R. Isothermal Vapor-Liquid Equilibrium for the Three Binary Systems 1,1,1,2,3,3Hexafluoropropane with Dimethyl Ether or Propane, and 1,1,1,3,3,3Hexafluoropropane with Dimethyl Ether. Fluid Phase Equilib. 2000, 174, 3. (32) Bobbo, S.; Fedele, L.; Camporese, R.; Stryjek, R. Hydrogen Bonding of HFCs with Dimethyl Ether Evaluation of Isothermal VLE Measurements. Fluid Phase Equilib. 2002, 199, 153. (33) Comun˜as, M. J.; Baylaucq, A.; Boned, C.; Canet, X.; Fernandez, J. High-Pressure Volumetric Behavior of x1,1,1,2Tetrafluoroethane + (1 - x)2,5,8,11,14-Pentaoxapentadecane (TEGDME) Mixtures. J. Chem. Eng. Data 2002, 47, 233. (34) Comun˜as, M. J. P.; Ferna´ndez, J.; Baylaucq, A.; Canet, X.; Boned, C. PFTx Measurements for HFC-134a + Triethylene Glycol Dimethylether System. Fluid Phase Equilib. 2002, 199, 185. (35) Clever, H. L.; Battino, R. The Solubility of Gases in Liquids, Techniques of Chemistry; J. Wiley & Sons: New York, 1975. (36) Wilhelm, R.; Battino, R.; Wilcock, J. Low-Pressure Solubility of Gases in Liquid Water. Chem. Rev. 1977, 77, 219. (37) Mainar, A. M.; Pardo, J. I.; Santafe´, J.; Urieta, J. S. Solubility in Binary Liquid Mixtures: An Experimental and Theoretical Study of the System Noble Gas + Trifluoroethanol + Water. Ind Eng. Chem. Res. 2003, 42, 1439. (38) Fredenslund, A.; Jones, R. L.; Prausnitz, J. M. GroupContribution Estimation of Activity Coefficients in Nonideal Liquid Mixtures. AIChE J. 1975, 21, 1086. (39) Gmehling, J.; Li, J.; Schiller, M. A. Modified UNIFAC Model. 2. Present Parameter Matrix and Results for Different Thermodynamic Properties. Ind. Eng. Chem. Res. 1993, 32, 178. (40) Kiepe, J.; Horstmann, S.; Fischer, K.; Gmehling, J. Experimental Determination and Prediction of Gas Solubility Data for CO2 + H2O Mixtures Containing NaCl or KCl at Temperatures between 313 and 393 K and Pressures up to 10 MPa. Ind. Eng. Chem. Res. 2002, 41, 4393.
Received for review July 24, 2003 Revised manuscript received December 17, 2003 Accepted January 5, 2004 IE030623W
